The thing about exercising helping with depression is crap. Subsequent studies have not been able to replicate those results. Some people get a short term lift out of it (not everyone gets the endorphin reaction, and apparently that's particularly common for people with AD/HD, which I have), but long-term effects for depressed people are actually quite rare.
For upper-body strength: Try isometrics, including but not limited to yoga. No equipment required. Doesn't build muscle bulk the way weightlifting does, but absolutely will increase strength. And easier on the body, although you'll still ache after a hard workout. But! The thing is that you can start with just a couple of simple things that you make part of your daily routine. Yoga balancing exercises (the simplest are probably tree pose, where you stand on one foot with your hands pressed together in front of your sternum; and table balances, where you get down on all fours, make your back as level as possible, then extend one arm and the opposite leg and hold) strengthen core muscles, and you work up slowly. Start at, oh, eight or ten slow breaths, and when you can easily hold it that long, you add a couple more breaths. Very little soreness. I do a few yoga poses every morning and evening as part of my daily ritual practice. There are other things than yoga as well, if yoga isn't your thing, it's just the one I know a little about. But strengthening your core muscles will help support you in other kinds of exercise and decrease the stress on your body.
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For upper-body strength: Try isometrics, including but not limited to yoga. No equipment required. Doesn't build muscle bulk the way weightlifting does, but absolutely will increase strength. And easier on the body, although you'll still ache after a hard workout. But! The thing is that you can start with just a couple of simple things that you make part of your daily routine. Yoga balancing exercises (the simplest are probably tree pose, where you stand on one foot with your hands pressed together in front of your sternum; and table balances, where you get down on all fours, make your back as level as possible, then extend one arm and the opposite leg and hold) strengthen core muscles, and you work up slowly. Start at, oh, eight or ten slow breaths, and when you can easily hold it that long, you add a couple more breaths. Very little soreness. I do a few yoga poses every morning and evening as part of my daily ritual practice. There are other things than yoga as well, if yoga isn't your thing, it's just the one I know a little about. But strengthening your core muscles will help support you in other kinds of exercise and decrease the stress on your body.